Tips on removing old veneer?

I have my grandmother’s old bedroom set. Most of the suite is still in use but the bed itself, headboard and footboard, is beyond repair. They don’t really have any value other than sentimental and I’d like to do something with the wood besides just chucking it because, under the badly scarred mahogany veneer, there are what appear to be some nicely figured and wide maple boards.

With my 5th anniversary coming up in October, and the 5th being “wood” if you’re a traditional kind of guy (and I am), I thought I’d use the reclaimed wood to make a jewelry case for my wife to house the various “pretties” I’ve bought for her over the years.

So my question is: What’s the best way to go about removing the veneer? I know I need to get it, and the adhesive, removed as much as possible before I start machining the wood. I shudder to think what it would do to my planer if I put it through as-is. Since the bed would have been made in the 1930’s I feel reasonably safe assuming it was secured with hide glue. Anyone have any tips? I can probably chip or peel off most of the actual veneer since it’s come loose in a lot of places, but what to do about making sure I get it all, and the accompanying adhesive residue, off of the wood before I start planning it smooth? Is there a reasonably easy way (easy meaning not involving a ton of chemicals and a HazMat suit, I’m not adverse to using elbow) to get the stuff off or should I maybe take it to my local lumber supplier and pay them to run the boards through their drum sander?

-- We may never know who let the dogs out, but I'd bet anything PETA was involved.